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Chinese Physics Letters

Absorption Spectra of a Three-Level Atom Embedded in a PBG Reservoir

Han Zhang, Ke Zhang, Hanzhuang Zhang

Published Apr 1, 2007• 10 citations
Publisher

Abstract

We introduce the `decay rate' terms into the density matrix equations of an atom embedded in a photonic band gap (PBG) reservoir successfully. By utilizing the master equations, the probe absorption spectra and the refractivity properties of a three-level atom in the PBG reservoir are obtained. The interaction between the atom and the PBG reservoir as well as the effects of the quantum interference on the absorption of the atom has also been taken into account. It is interesting that two different types of the anomalous dispersion relations of refractivity are exhibited in one dispersion line. The methodology used here can be applied to theoretical investigation of quantum interference effects of other atomic models embedded in a PBG reservoir.

DOI
10.1088/0256-307x/24/4/024

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We introduce the `decay rate' terms into the density matrix equations of an atom embedded in a photonic band gap (PBG) reservoir successfully. By utilizing the master equations, the probe absorption spectra and the refractivity properties of a three-level atom in the PBG reservoir are obtained. The interaction between the atom and the PBG reservoir as well as the effects of the quantum interference on the absorption of the atom has also been taken into account. It is interesting that two different types of the anomalous dispersion relations of refractivity are exhibited in one dispersion line. The methodology used here can be applied to theoretical investigation of quantum interference effects of other atomic models embedded in a PBG reservoir.
The probe absorption-dispersion spectra of a radio-frequency (RF)-driven five-level atom embedded in a photonic crystal are investigated by considering the isotropic double-band photonic-band-gap (PBG) reservoir. In the model used, the two transitions are, respectively, coupled by the upper and lower bands in such a PBG material, thus leading to some curious phenomena. Numerical simulations are performed for the optical spectra. It is found that when one transition frequency is inside the band gap and the other is outside the gap, there emerge three peaks in the absorption spectra. However, for the case that two transition frequencies lie inside or outside the band gap, the spectra display four absorption profiles. Especially, there appear two sharp peaks in the spectra when both transition frequencies exist inside the band gap. The influences of the intensity and frequency of the RF-driven field on the absorptive and dispersive response are analyzed under different band-edge positions. It is found that a transparency window appears in the absorption spectra and is accompanied by a very steep variation of the dispersion profile by adjusting system parameters. These results show that the absorption-dispersion properties of the system depend strongly on the RF-induced quantum interference and the density of states (DOS) of the PBG reservoir.
The probe absorption-dispersion spectrum of a double V-type four-level atom in a double-band photonic crystal is investigated. In the model used, the double V-type transitions are, respectively, coupled by the free vacuum modes and the photonic band gap modes, leading to the two possible types of quantum interference. Three types of zero absorption (transparency) appear in this model. In the first type, there exist two zeroes at the band edge frequencies in the case of isotropic photonic band gap. In the second type, a zero emerges at the middle frequency of two upper levels in the case that the quantum interference takes place in both V-type transitions. Finally, in the third type, a zero occurs at or around the middle frequency of two upper levels in the case that the quantum interference takes place only in the V-type transitions coupled to the free vacuum modes. Ultimately, the probe absorption-dispersion spectrum in the case of the single-band photonic band gap reservoirs compared to those of the double-band photonic band gap reservoirs. The results show that the dispersion property of the system depends on the two types of the quantum interference and the density of states of the photonic band gap reservoir.
The two models of three-level (one upper level and two lower levels, or two upper levels and one lower level) atom embedded in a double-band photonic crystal are adopted. The atomic transitions from the upper levels to the lower levels are assumed to be coupled by the same reservoir which are respectively the isotropic photonic band gap (PBG) modes, the anisotropic PBG modes and the free vacuum modes. The effects of the fine structure of the atomic ground state levels in the model with one upper level and two lower levels and the quantum interferences in the model with two upper levels and one lower level on the spontaneous emission spectrum of an atom are investigated in detail. Most interestingly, it is shown that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PBG case. The quantum interferences induce additional narrow spontaneous lines near the transition from the empty upper level to the lower level.
Two models (an upper levels coupling model and a lower levels coupling model) of a four-level atom embedded in a double-band photonic crystal are adopted. The effect of spontaneous emission cancellation of such systems embedded in different reservoirs are investigated. Especially, the "trapping conditions" of such systems in photonic band gap (PBG) reservoirs are discussed for the first time. We also investigate the different quantum interference effects of the lower levels coupling model embedded in an isotropic PBG reservoir. It is interesting that when the trapping conditions are fulfilled, the additional peaks, which result from the contribution of the additional singularities of Laplace transform of the delayed Green function of the isotropic PBG modes, are eliminated.PACS Nos.: 42.50.Gy, 42.50.Ct, 42.70.Qs
The absorption–dispersion properties of a microwave-driven five-level atom embedded in an isotropic photonic bandgap (PBG) have been studied. Due to the singular density of modes (DOM) in the isotropic PBG and the dynamically coherence induced by the coupling fields, modified reservoir-induced transparency and quantum interference-induced transparency emerge simultaneously. Their interaction leads to ultra-narrow spectral structure. As a result of closed-loop configuration, these features can be manipulated by the amplitudes and relative phase of the coherently driven fields. The position and width of PBG also have an influence on the spectra. The theoretical studies can provide us with more efficient methods to control the atomic absorption–dispersion properties, which have applications in optical switching and slow light.
The effect of atomic position on the spontaneous emission and optical spectra of a three-level atom embedded in a photonic crystal was studied by considering the coherent two-band photonic-band-gap (PBG) reservoir. With the definite phase difference between the fields of the air band and dielectric band in this coherent PBG reservoir, we found that this coherent property grows stronger and results in the spectrum shift and the appearance of dark lines and kinks as the width of band gap gets smaller; and the variation of the atomic position leads to large shift of spectral peak. The averaged spectra of the system with an ensemble of atoms embedded in the dielectric region are blueshifted while those of atoms in the air region are redshifted. The spectra peaks can even shift more than 75% of the half width at half maximum. The feasible experimental systems composed of an ensemble of molecules (quantum dots or fluorescence dye) in photonic crystals are discussed.